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Unbiased Estimation and Statistical Analysis of 3-D Rigid Motion from Two Views
January 1993 (vol. 15 no. 1)
pp. 37-50

The problem of estimating 3D rigid motion from point correspondences over two views is formulated as nonlinear least-squares (LS) optimization, and the statistical behaviors of the errors in the solution are analyzed by introducing a realistic model of noise described in terms of the covariance matrices of N-vectors. It is shown that the LS solution based on the epipolar constraint is statistically biased. The geometry of this bias is described in both quantitative and qualitative terms. Finally, an unbiased estimation scheme is presented, and random number simulations are conducted to observe its effectiveness.

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Index Terms:
3D rigid motion estimation; nonlinear least squares optimisation; image sequences; statistical analysis; covariance matrices; N-vectors; epipolar constraint; geometry; unbiased estimation; image sequences; motion estimation; optimisation; statistical analysis
Citation:
K. Kanatani, "Unbiased Estimation and Statistical Analysis of 3-D Rigid Motion from Two Views," IEEE Transactions on Pattern Analysis and Machine Intelligence, vol. 15, no. 1, pp. 37-50, Jan. 1993, doi:10.1109/34.184773
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